Two Column Solution

Linear Relations Lesson Plan

Linear Relations Lesson Plan

Subject: Mathematics Grade:    8	Lesson Number:    7  of  8 Time: 15 minutes
Big Idea or Question for the Lesson: What is an ordered pair? What is a linear relation?
PLO foci for this lesson: B1 graph and analyse two-variable linear relations [C, ME, PS, R, T, V]
Objectives: Students will be able to  (SWBATs) determine the missing value in an ordered pair for a given equation create a table of values by substituting values for a variable in the equation of a given linear relation describe the relationship between the variables of a given graph construct a graph from the equation of a given linear relation (limited to discrete data)
Content and Language Objectives: -   understand what an ordered pair is (verbal) -  determine what a linear relation is (verbal/kinesthetic)		Skills/Strategies required: -  understand what a variable represents -  be able to solve for a variable in a given equation
Materials/resources: masking tape sharpie/thick pen whiteboard/markers Graph paper to hand to students
Assessment Plan: formative assessment: visually see if the students graphed their ordered pair correctly
Adaptations: [ for EALs] just make sure when you say, “variable”, you point specifically to the variable, and same goes for any integers skeleton note sheet that they fill in at the end of the lesson Modifications: [for slower processors] skeleton note sheet that they fill in at the end of the lesson Extensions: [ for the ‘quick study’ folk] graphing negative slopes, or more complicated functions (individually on their own graph paper)
Hook and Introduction (2 min) (__:__ - __:__) PREPARE THE FLOOR! review that they know what variables are and such hook for full lesson (graph “spicy vs parachute” ask Alison) Development (about 15 min) (__:__ - __:__) - Teacher-led (10 min) (__:__ - __:__) - Class/Group Activity (__:__ - __:__) Ian: Today we are going to look at linear relations (draw on board). Everyone should pair up and tell everyone to pick an integer from -3 to 3 but you cannot repeat a number that someone else chose (throw the stuffy at them as they choose). An evil wizard kidnaps your stuffy. He locks your animal in a dungeon. You need to rescue it! But you don’t know where they are. Alison: You only are given two clues: (1) your stuffy’s cell number (x-coordinate), which is the number they chose, and (2) a cipher that represents a map of where all the cells are (explain this). Find your animal by finding the y-coordinate of its cell. Ian: This wizard has bamboozled us! Let’s try and figure out how to use this cypher. Take a look at this grid below us. This line is labelled x. Let’s all find our places on the x number line and place your stuffys there for now. Because this dungeon is this whole grid, we have this up down or y direction. In order to find out where your cell and your animal is in the y direction, we must find our y values! How can we do this?! Questions: how can you find the y coordinate using your x value? How can you show this visually on the map/grid of the evil wizard’s lair? What order should we rescue the animals so we’re the fastest? Now give students time to solve for their y value, and place their stuffy on the grid taped to the floor where they think their cell is Alison: Now open up a discussion of what the shape of the graph looks like, because it’s actually continuous between each person (object). Hint: It’s a straight line. It’s a straight line! So! What does the class think Linear means? If this equation is a two variable LINEAR equation, and it comes up with a straight line, thennnn!’ So each of you has an x value that you chose, and a y value that you figured out using the equation we gave you. What you did when you got those two values is figured out an ordered pair. Conventionally, we write it as such (x,y). This is arbitrary.Get everyone to represent their coordinates as ordered pairs, and then collect them all on the board. Now… level two! Independent Work (  :   )-( :  ) (5 mins) Ian: Move to independent work, now LEVEL 2! You are now all kidnapped and placed in new cells!  But now you have a different cipher to figure out where everyone’s animals are (cell numbers are -3 to 3)! (Hand out the ciphers as scrolls) Create a list of ordered pairs (like we did on the board) and then plot them on graph paper (individually). cipher: y= -3x+2 Hand out graph paper, scrolls, and have students create a list of ordered pairs to figure out where everyone else’s cells are (with x values -3 to 3) and then plot them on the graph paper (figure out their y values). Closing (1 min) (__:__ - __:__) Now we all know what linear means and how to graph when given an x value! Could you figure the graph out if given a y value? ALSO DO YOUR HOMEWORK!

Brief Review of David Hewitt's In Class Methods

Adding and subtract whole numbers:
I thought this was a great use of classroom space, a great way to keep students engaged (as they clearly were), and the choral speaking was an inspiring way to get instant feedback if everyone is understanding or not.

I'm Thinking Of A Number:
This was so brilliant; such an elegant way of teaching about solving one variable equations. Posing it the way he did made it seem like a magic trick, or a game, so students were immediately interested and consistently engaged. His syncing of his words and what he wrote down was a great way to use both visual and audio cues to teach. He also used repetition fairly frequently, which I think benefited this particular strategy very much. I loved it. I am absolutely going to use this (or a modified version of it) when I teach algebra during my long practicum.

SNAP Fair Review

This was taken from an email I wrote to the organizer of the SNAP Math Fair, it is slightly editted to change pronouns etc:

Great job with the SNAP fair today! It was really great and the students were so enthusiastic about their projects! I think it really goes to show how far [the organizers have] gone in terms of student centered approach. [The students] took such pride and ownership of their set up, presentation, and location in terms of their choice of Anthropology exhibit. I had several students tell me to "Go check out this person's presentation, you'll love it", clear example of how non-competitive and, in fact, celebratory this fair is. Students were just so enthusiastic about the math. The all-inclusive aspect was great as all types of mathematicians could be represented in their problems: logic, patterns, relations, arithmetic etc. And I didn't even get to see them all! The problem based approach is such a great avenue for students to explore problems that they love and gave me great ideas for puzzles to use in my classroom, which is just so exciting for me!

Arbitrary vs Necessary Article

"All students will need to be informed of the arbitrary. However, the necessary is dependent upon the awareness that the students already have"
Arbitrary facts are things that a student would not be able to figure out on his/her own. Necessary facts are things that a student MIGHT be able to figure out on his/her own. Certain conventions, such as the (x,y) placement of coordinates on the Cartesian plane, are arbitrary. A student would not be able to come to the same conclusion on his/her own. However, a student might be able to figure out a calculation of a side length of a triangle without guidance from a teacher; this is a necessary fact, according to Hewitt.
In a particular lesson, deciding what is necessary depends on any particular class on a given day. The arbitrary things are probably things that I don't even really know why the convention is there, or how to explain. The arbitrary stuff, I will "do the math", and teach explicitly. The necessary stuff, I will guide the students into figuring out themselves. That's the plan, at least.

SNAP Math Fair

I love the principals behind SNAP fairs; the intentions, implementation, and goals illustrated in the Math fair booklet are inspiring. I believe the principals can expand beyond the Math Fair and apply to all aspects of my philosophy and pedagogy. Student centered, Non competitive, All inclusive, and Problem based. I love the whole approach. My lessons, exercises, and assessments should all be student centered. My assessments should be non competitive; the students should only be competitive against their past selves. My classroom should be all inclusive; as should my pedagogy. And, in order to make mathematics tangible and relate-able to the students, I believe the vast majority of my exercises and questions should be problem based.

I wonder of the logistics of implementing a SNAP math fair at my practicum school. I worry that I am going to struggle to personally survive the workload and preparation it takes to teach at 80% capacity. However, if I do find that I have the energy and time to put on a SNAP math fair, I would love to put one on as I think the whole approach could foster a lot of love for mathematics for presenters and participants alike.